I would say 3. Electromagnetic, Electrochemical and Static.
Electromagnetic would cover anything that uses a prime mover to turn a generator -
[Hydroelectric, Nuke generated steam, Fossil fuel generated steam, geothermic generated steam, internal combustion motors, wind, any other moving form of energy].
Electrochemical would cover naturally occuring differences in potential that result in a continuous current flow -
[Batteries, Drycells, disimmilar metallic contact, Lightning, Solar Cells, Thermocouples, Piezoelectric crystals, etc.].
Static would cover anything which one substance has an ability to scrape Electrons from another substance, hold these Electrons, concentrate them until a certain capacity was achieved, hold that concentration until discharge occured - which would drain Electrons until the potential difference between the two materials is once again equal. -
[this would cover carpet shocks, Van deGraaff Generators, Automobile tires, RFI induced on antennas, Plasmas started in discharge lamps, build up of charges on CRTs after degaussing coils used, any scraping of two different types of materials - one having a higher - potential, the other being either lower - or higher + potential, and the like].
3 basic ways - hundreds of inividual methods - all doing one thing: Moving Energy! Not creating it, nor getting rid of it - just moving it.
I guess the more familiar way known would be to break down like this:
That makes 6, but 4 of them fall in the same field when you get real indepth.
I suggest that, unless one wishes to become a major nerd, avoid figuring out why those 4 fall into the same field!
In a way, Lightning falls in both catagories - Electrochemical and Electromechanical [Electromagnetic], but does not fall in the Static catagory, since it is nothing at all like static electricity. It's more like pulsating DC.
I know I'm forgetting something, but just what!!
Quite sure this answer doesn't qualify me for the grand prize, but might put me in the race for 5th prize, possibly a toss up for the booby prize
I'll take the booby prize! then I can fill my booby prize trophy case.